If x > 0, prove that T - In (1+ x) > 2+2x

Q: Let P(x) = tln(t) dt. Use part 1 of the fundamental theorem of calculus to determine if P(x) is…

A: Given function is

Q: .2 is strictly monotone Prove by definition that the function b(x) = increasing on [0, ∞) and is…

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Q: Prove that f: R R where f (x) = |x| is neither injective surjective. nor

A: To prove this theorem, we use the defination of one one and onto.

Q: Prove that v = In (x- 2)^2+(y-N)^2 is harmonic in every region does not include the point (2,N) and…

A: Given v=lnx-22+y-N2 where N=44. So, v=lnx-22+y-442                                    ........1 To…

Q: • prove that y` = = for y= (of (1+x)) 1+x²

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Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)

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Q: If p(x) = p(t)dt, prove p must be the zero function. Hint: Fundamental Theorem of Calculus.

A: Fundamental theorem of calculus. Let f be a continuous function on [a,b] . If Fx=∫axftdt   then…

Q: ) Find a function f(x) satisfying these conditi

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Q: If x and y are elements of an ordered integral domain D,prove the following inequalities:   x2 + y2…

A: An ordered integral domain D is an integral domain with a subset of positive elements with the…

Q: Use Theorem 2 to show that 3, if x <-10 2, if – 10 sxso F:R → R,F(x) = -2, if 0< x< 10 -3, if x2 10…

A: so we have to show that given function is discontinuous at 2 and -2 (a)   Discontinuous  at -2…

Q: Show that f(x) = x5-x3-1 has at least one real zero between 1 and 2.

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Q: D. Prove that f(x) = |x - 6| is continuous at all points c in R.

A: Given function is fx=x−6. We have to prove that the function fx=x−6 is continuous at all point c in…

Q: Prove H'n(x) = 2nHn−1(x), n = 0, 1, . . .

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Q: Use the comparison theorem with f(x) = = 1 √x to show that [₂²= 1 √x-1 is divergent.

A: See this solution in below

Q: Determine the order of approximation for t

A: Polynomial Expansion: If no variable appears within parentheses and all like terms have been merged,…

Q: Let f(x) =x² t2X. Find all the values of ċ in the interval [2,0] such that f (c) =0.

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Q: f is increasing on (a, b) of for all x1, x2 in (a, b) when x1 less than x2,f(x1) less than f(x2).

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Q: Prove that f (x) = x-12 is : (i) not sectionally continuous in every finite interval in the

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Q: Use Euler’s Theorem to find the degree of homogeneity for f( x1 , x2) = x3 + y3 + 3xy2

A: We will use the Euler's theorem which is : x•fx + y•fy = nf  Where, n = degree of homogeneity    The…

Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x&lt;0   So,…

Q: Consider the function f(x) = In(x) – arctan(2.x). 2 a. Determine all critical points in the domain…

A: We know that the critical points of a function are those points at which the first derivative is…

Q: 4. Let f be defined for all real x, and suppose that \fx) – f(v)| < (x – y)? for all x, y e R. Prove…

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Q: Find the domain of the function. h(x) = In x + In(2 - x)

A: Given h(x)=ln x+ln (2-x) Find the domain by finding where the expression is defined.

Q: 3. Use the Intermediate Value Theorem to show that f(a) = a2-3x +1 has at least one real zero…

A: According to intermediate value theorem, if f(x) is a continuous function whose domains contains the…

Q: 14) Use the Intermediate Value Theorem to show that the po zero in the given interval. g(x) = 2x³ –…

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Q: Prove that f(x) = other than the graphing method. x² – 1 is continuous at c = 0 by any method |

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Q: Show that f (x) = 3x² - x - 1 is O(x²) with suitable C and k.

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Q: Find the domain of the function. k(x) = In |x|

A: The domain of a function, f(x)  is the set of input values of x for which f(x) is real and defined.

Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: (a) Prove that if m ₹ N, then the function f(x) = xm is continuous on R.

A: We have to prove that, the function f(x) = xm,   m∈ℕ  is continuous on ℝ.

Q: Using R, use antithetic variables to estimate the following: In(1+ x2) dt x2

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Q: Suppose that f (0) = 2 and f' (x) ≤ 3 for x &gt; 0. Apply the MVT to the interval [0, 4] to prove…

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Q: Verify that f(x)=x2+1/x satisfies the hypotheses of the Rolle's Theorem on the interval [1/2 2] and…

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Q: 1, when x is a rational number. f(x)= 0, when x is not a rational number. Determine if the function…

A: Given:  fx=1, when x is a rational0,  when x is not a rational To determine the function  f is…

Q: Use the definition to prove that the function in f(x) = 2x - 3 is uniformly continuous.

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Q: Let ƒ(x) = px2 + qx + r be a quadratic function defined on a closed interval [a, b] . Show that…

A: Given,

Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: Find the absolute maximum and the absolute minimum of U(q) 20002 (15 5q)4 on the nterval 04.

A: First find the derivative of the given function and compute the critical points.

Q: A continuous real-valued function f (x) with f (a) ƒ (b) < 0 , has at least one root in [a, b]

A: This question is related to Real Analysis.

Q: Use the intermediate value theorem to show that f(x) = (e^−x^2)−x has at least one root in the…

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Q: Let g(x) = x². Which of the following outputs of g is not guaranteed by the Intermediate Value…

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Q: Use the intermediate value theorem to show that f(x) = e −x 2 − x has at least one root in the…

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Q: Determine if f(x)=In (x² + 1) is uniformly continous on the interval I (-0, +0)

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Q: The domain of the finction f(x, y) = In(-x² - +1) is:

A: The domain of a function is the range of the values that can be input into the function. The…

Q: If f(x)=x^3/3 -3x Show that f(x) satisfies the hypothesis of the Roll's Theorem on the interval [-3,…

A: Topic:- rolls theorem

Q: Use the IVT to find an interval of length 0.3 that contains a root of In r = 3 – 2r.

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Q: Prove: f(x)=5x y is continuous at x=2

A: A function fx is continuous at a point x=a, if limx→afx=fa Given function is

Q: Let f(x) = 2 cosh(4x) – e4x %3D Find the absolute maximum of f(x) on the interval [0, In 3].

A: The given function is                                         f(x)=2 cosh(4x)-e-4x We know that…

Q: Use the e-d definition to prove that f(x) = x³ + 3 is continuous at xo = 3.

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Q: Show that f (r) = x³ – 3x2 + 2 is monotonically increasing on every interval.

A: Given that: f(x)=x3-3x2+2